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22 6 8a a

Solve the equation:

Given

Write down f(x) in the forms:

a)

b)

c) Write down the equation of the axis of symmetry of the graph.

22 8 10f x x x

22f x x h k

2f x x p x q

Consider the curve

Find the transformations of this curve

where:

xxxxf 23 2

1xfxg

12 xfxh

2 3 0

2

x y

x y

Solve the simultaneous equations

2 3 15)

10

x y

x y

e eb

e e

a)

Find the sum of the first 30 terms of the

sequence 3, 5, 7, 9, …

Find the following sums

1

20

5

15

1

2.0)

2.3320)

523)

n

n

n

n

n

c

b

na

Find the numbers in the 6th row of

Pascal’s triangle:

5 5 5 5 5 5

0 1 2 3 4 5

Evaluate the following:

Find the coefficient of x5 in the

expansion of 7(2 3)x

Solve the equations:

223)1ln( xexx

523 3 xexxa)

b)

Consider the function

Draw the tangent to the curve at x=0 and

give its equation.

Find the other point of intersection of this

tangent with the curve.

5075 23 xxxxf

8) Find the equation of the tangent

and normal at x =3 of the following

function:

xxxxf 105.05.0 23

Find the area between the curve

and the x-axis .( 6)y x x

Represent on the same pair of axes f(x),

its inverse function and the line y=x.

3xexf

Consider the function

(a) Write down the equations of the asymptotes to the

graph of

(b) Find the set of values of for which

(c) Find the gradient at -5

(d) Explain why for any value of x.

2 6

3

xf x

x

f x

0f x

0f x

Given and 3 2 2xf x x e ln 1g x x

a. Write down the domain of g.

b. Sketch the graph of f for f(x) >0

c. Write down the coordinates of the maximum point on the

graph of f.

d. Find

e. Find the x-coordinate of the points at which the graphs of

f and g have the same gradient in the interval 0<x<1.5

limx

f x

On the same pair of coordinate

axes draw the graphs of the function

f(x) and its inverse function if.

10ln xxf

State the domain of f(x) and its inverse.

) 5 2xc e x

1) 1

1 2

xa

x x

Solve the equations

1) lnb x e

x